// Copyright (c) 2021, gottingen group.
// All rights reserved.
// Created by liyinbin lijippy@163.com

#include "abel/random/zipf_distribution.h"

#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <iterator>
#include <random>
#include <string>
#include <utility>
#include <vector>

#include "gmock/gmock.h"
#include "gtest/gtest.h"
#include "abel/log/logging.h"
#include "testing/chi_square.h"
#include "abel/random/engine/sequence_urbg.h"
#include "abel/random/random.h"
#include "abel/strings/str_cat.h"
#include "abel/strings/str_replace.h"
#include "abel/strings/strip.h"

namespace {

    using ::abel::random_internal::kChiSquared;
    using ::testing::ElementsAre;

    template<typename IntType>
    class ZipfDistributionTypedTest : public ::testing::Test {
    };

    using IntTypes = ::testing::Types<int, int8_t, int16_t, int32_t, int64_t,
            uint8_t, uint16_t, uint32_t, uint64_t>;
    TYPED_TEST_CASE
    (ZipfDistributionTypedTest, IntTypes);

    TYPED_TEST(ZipfDistributionTypedTest, SerializeTest) {
        using param_type = typename abel::zipf_distribution<TypeParam>::param_type;

        constexpr int kCount = 1000;
        abel::insecure_bit_gen gen;
        for (const auto &param : {
                param_type(),
                param_type(32),
                param_type(100, 3, 2),
                param_type(std::numeric_limits<TypeParam>::max(), 4, 3),
                param_type(std::numeric_limits<TypeParam>::max() / 2),
        }) {
            // Validate parameters.
            const auto k = param.k();
            const auto q = param.q();
            const auto v = param.v();

            abel::zipf_distribution<TypeParam> before(k, q, v);
            EXPECT_EQ(before.k(), param.k());
            EXPECT_EQ(before.q(), param.q());
            EXPECT_EQ(before.v(), param.v());

            {
                abel::zipf_distribution<TypeParam> via_param(param);
                EXPECT_EQ(via_param, before);
            }

            // Validate stream serialization.
            std::stringstream ss;
            ss << before;
            abel::zipf_distribution<TypeParam> after(4, 5.5, 4.4);

            EXPECT_NE(before.k(), after.k());
            EXPECT_NE(before.q(), after.q());
            EXPECT_NE(before.v(), after.v());
            EXPECT_NE(before.param(), after.param());
            EXPECT_NE(before, after);

            ss >> after;

            EXPECT_EQ(before.k(), after.k());
            EXPECT_EQ(before.q(), after.q());
            EXPECT_EQ(before.v(), after.v());
            EXPECT_EQ(before.param(), after.param());
            EXPECT_EQ(before, after);

            // Smoke test.
            auto sample_min = after.max();
            auto sample_max = after.min();
            for (int i = 0; i < kCount; i++) {
                auto sample = after(gen);
                EXPECT_GE(sample, after.min());
                EXPECT_LE(sample, after.max());
                if (sample > sample_max) sample_max = sample;
                if (sample < sample_min) sample_min = sample;
            }
            DLOG_INFO(
                              abel::string_cat("Range: ", +sample_min, ", ", +sample_max));
        }
    }

    class ZipfModel {
    public:
        ZipfModel(size_t k, double q, double v) : k_(k), q_(q), v_(v) {}

        double mean() const { return mean_; }

        // For the other moments of the Zipf distribution, see, for example,
        // http://mathworld.wolfram.com/ZipfDistribution.html

        // PMF(k) = (1 / k^s) / H(N,s)
        // Returns the probability that any single invocation returns k.
        double PMF(size_t i) { return i >= hnq_.size() ? 0.0 : hnq_[i] / sum_hnq_; }

        // CDF = H(k, s) / H(N,s)
        double CDF(size_t i) {
            if (i >= hnq_.size()) {
                return 1.0;
            }
            auto it = std::begin(hnq_);
            double h = 0.0;
            for (const auto end = it; it != end; it++) {
                h += *it;
            }
            return h / sum_hnq_;
        }

        // The InverseCDF returns the k values which bound p on the upper and lower
        // bound. Since there is no closed-form solution, this is implemented as a
        // bisction of the cdf.
        std::pair<size_t, size_t> InverseCDF(double p) {
            size_t min = 0;
            size_t max = hnq_.size();
            while (max > min + 1) {
                size_t target = (max + min) >> 1;
                double x = CDF(target);
                if (x > p) {
                    max = target;
                } else {
                    min = target;
                }
            }
            return {min, max};
        }

        // Compute the probability totals, which are based on the generalized harmonic
        // number, H(N,s).
        //   H(N,s) == SUM(k=1..N, 1 / k^s)
        //
        // In the limit, H(N,s) == zetac(s) + 1.
        //
        // NOTE: The mean of a zipf distribution could be computed here as well.
        // Mean :=  H(N, s-1) / H(N,s).
        // Given the parameter v = 1, this gives the following function:
        // (Hn(100, 1) - Hn(1,1)) / (Hn(100,2) - Hn(1,2)) = 6.5944
        //
        void Init() {
            if (!hnq_.empty()) {
                return;
            }
            hnq_.clear();
            hnq_.reserve(std::min(k_, size_t{1000}));

            sum_hnq_ = 0;
            double qm1 = q_ - 1.0;
            double sum_hnq_m1 = 0;
            for (size_t i = 0; i < k_; i++) {
                // Partial n-th generalized harmonic number
                const double x = v_ + i;

                // H(n, q-1)
                const double hnqm1 =
                        (q_ == 2.0) ? (1.0 / x)
                                    : (q_ == 3.0) ? (1.0 / (x * x)) : std::pow(x, -qm1);
                sum_hnq_m1 += hnqm1;

                // H(n, q)
                const double hnq =
                        (q_ == 2.0) ? (1.0 / (x * x))
                                    : (q_ == 3.0) ? (1.0 / (x * x * x)) : std::pow(x, -q_);
                sum_hnq_ += hnq;
                hnq_.push_back(hnq);
                if (i > 1000 && hnq <= 1e-10) {
                    // The harmonic number is too small.
                    break;
                }
            }
            assert(sum_hnq_ > 0);
            mean_ = sum_hnq_m1 / sum_hnq_;
        }

    private:
        const size_t k_;
        const double q_;
        const double v_;

        double mean_;
        std::vector<double> hnq_;
        double sum_hnq_;
    };

    using zipf_u64 = abel::zipf_distribution<uint64_t>;

    class ZipfTest : public testing::TestWithParam<zipf_u64::param_type>,
                     public ZipfModel {
    public:
        ZipfTest() : ZipfModel(GetParam().k(), GetParam().q(), GetParam().v()) {}

        abel::insecure_bit_gen rng_;
    };

    TEST_P(ZipfTest, ChiSquaredTest) {
        const auto &param = GetParam();
        Init();

        size_t trials = 10000;

        // Find the split-points for the buckets.
        std::vector<size_t> points;
        std::vector<double> expected;
        {
            double last_cdf = 0.0;
            double min_p = 1.0;
            for (double p = 0.01; p < 1.0; p += 0.01) {
                auto x = InverseCDF(p);
                if (points.empty() || points.back() < x.second) {
                    const double p = CDF(x.second);
                    points.push_back(x.second);
                    double q = p - last_cdf;
                    expected.push_back(q);
                    last_cdf = p;
                    if (q < min_p) {
                        min_p = q;
                    }
                }
            }
            if (last_cdf < 0.999) {
                points.push_back(std::numeric_limits<size_t>::max());
                double q = 1.0 - last_cdf;
                expected.push_back(q);
                if (q < min_p) {
                    min_p = q;
                }
            } else {
                points.back() = std::numeric_limits<size_t>::max();
                expected.back() += (1.0 - last_cdf);
            }
            // The Chi-Squared score is not completely scale-invariant; it works best
            // when the small values are in the small digits.
            trials = static_cast<size_t>(8.0 / min_p);
        }
        ASSERT_GT(points.size(), 0);

        // Generate n variates and fill the counts vector with the count of their
        // occurrences.
        std::vector<int64_t> buckets(points.size(), 0);
        double avg = 0;
        {
            zipf_u64 dis(param);
            for (size_t i = 0; i < trials; i++) {
                uint64_t x = dis(rng_);
                ASSERT_LE(x, dis.max());
                ASSERT_GE(x, dis.min());
                avg += static_cast<double>(x);
                auto it = std::upper_bound(std::begin(points), std::end(points),
                                           static_cast<size_t>(x));
                buckets[std::distance(std::begin(points), it)]++;
            }
            avg = avg / static_cast<double>(trials);
        }

        // Validate the output using the Chi-Squared test.
        for (auto &e : expected) {
            e *= trials;
        }

        // The null-hypothesis is that the distribution is a poisson distribution with
        // the provided mean (not estimated from the data).
        const int dof = static_cast<int>(expected.size()) - 1;

        // NOTE: This test runs about 15x per invocation, so a value of 0.9995 is
        // approximately correct for a test suite failure rate of 1 in 100.  In
        // practice we see failures slightly higher than that.
        const double threshold = abel::random_internal::chi_square_value(dof, 0.9999);

        const double chi_square = abel::random_internal::chi_square(
                std::begin(buckets), std::end(buckets), std::begin(expected),
                std::end(expected));

        const double p_actual =
                abel::random_internal::chi_square_p_value(chi_square, dof);

        // Log if the chi_squared value is above the threshold.
        if (chi_square > threshold) {
            DLOG_INFO( "values");
            for (size_t i = 0; i < expected.size(); i++) {
                DLOG_INFO( abel::string_cat(points[i], ": ", buckets[i],
                                                         " vs. E=", expected[i]));
            }
            DLOG_INFO(abel::string_cat("trials ", trials));
            DLOG_INFO(
                              abel::string_cat("mean ", avg, " vs. expected ", mean()));
            DLOG_INFO( abel::string_cat(kChiSquared, "(data, ", dof, ") = ",
                                                     chi_square, " (", p_actual, ")"));
            DLOG_INFO(
                              abel::string_cat(kChiSquared, " @ 0.9995 = ", threshold));
            FAIL() << kChiSquared << " value of " << chi_square
                   << " is above the threshold.";
        }
    }

    std::vector<zipf_u64::param_type> GenParams() {
        using param = zipf_u64::param_type;
        const auto k = param().k();
        const auto q = param().q();
        const auto v = param().v();
        const uint64_t k2 = 1 << 10;
        return std::vector<zipf_u64::param_type>{
                // Default
                param(k, q, v),
                // vary K
                param(4, q, v), param(1 << 4, q, v), param(k2, q, v),
                // vary V
                param(k2, q, 0.5), param(k2, q, 1.5), param(k2, q, 2.5), param(k2, q, 10),
                // vary Q
                param(k2, 1.5, v), param(k2, 3, v), param(k2, 5, v), param(k2, 10, v),
                // Vary V & Q
                param(k2, 1.5, 0.5), param(k2, 3, 1.5), param(k, 10, 10)};
    }

    std::string ParamName(
            const ::testing::TestParamInfo<zipf_u64::param_type> &info) {
        const auto &p = info.param;
        std::string name = abel::string_cat("k_", p.k(), "__q_", abel::SixDigits(p.q()),
                                            "__v_", abel::SixDigits(p.v()));
        return abel::string_replace_all(name, {{"+", "_"},
                                               {"-", "_"},
                                               {".", "_"}});
    }

    INSTANTIATE_TEST_SUITE_P(All, ZipfTest, ::testing::ValuesIn(GenParams()),
                             ParamName);

// NOTE: abel::zipf_distribution is not guaranteed to be stable.
    TEST(ZipfDistributionTest, StabilityTest) {
        // abel::zipf_distribution stability relies on
        // abel::uniform_real_distribution, std::log, std::exp, std::log1p
        abel::random_internal::sequence_urbg urbg(
                {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
                 0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
                 0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
                 0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});

        std::vector<int> output(10);

        {
            abel::zipf_distribution<int32_t> dist;
            std::generate(std::begin(output), std::end(output),
                          [&] { return dist(urbg); });
            EXPECT_THAT(output, ElementsAre(10031, 0, 0, 3, 6, 0, 7, 47, 0, 0));
        }
        urbg.reset();
        {
            abel::zipf_distribution<int32_t> dist(std::numeric_limits<int32_t>::max(),
                                                  3.3);
            std::generate(std::begin(output), std::end(output),
                          [&] { return dist(urbg); });
            EXPECT_THAT(output, ElementsAre(44, 0, 0, 0, 0, 1, 0, 1, 3, 0));
        }
    }

    TEST(ZipfDistributionTest, AlgorithmBounds) {
        abel::zipf_distribution<int32_t> dist;

        // Small values from abel::uniform_real_distribution map to larger Zipf
        // distribution values.
        const std::pair<uint64_t, int32_t> kInputs[] = {
                {0xffffffffffffffff, 0x0},
                {0x7fffffffffffffff, 0x0},
                {0x3ffffffffffffffb, 0x1},
                {0x1ffffffffffffffd, 0x4},
                {0xffffffffffffffe,  0x9},
                {0x7ffffffffffffff,  0x12},
                {0x3ffffffffffffff,  0x25},
                {0x1ffffffffffffff,  0x4c},
                {0xffffffffffffff,   0x99},
                {0x7fffffffffffff,   0x132},
                {0x3fffffffffffff,   0x265},
                {0x1fffffffffffff,   0x4cc},
                {0xfffffffffffff,    0x999},
                {0x7ffffffffffff,    0x1332},
                {0x3ffffffffffff,    0x2665},
                {0x1ffffffffffff,    0x4ccc},
                {0xffffffffffff,     0x9998},
                {0x7fffffffffff,     0x1332f},
                {0x3fffffffffff,     0x2665a},
                {0x1fffffffffff,     0x4cc9e},
                {0xfffffffffff,      0x998e0},
                {0x7ffffffffff,      0x133051},
                {0x3ffffffffff,      0x265ae4},
                {0x1ffffffffff,      0x4c9ed3},
                {0xffffffffff,       0x98e223},
                {0x7fffffffff,       0x13058c4},
                {0x3fffffffff,       0x25b178e},
                {0x1fffffffff,       0x4a062b2},
                {0xfffffffff,        0x8ee23b8},
                {0x7ffffffff,        0x10b21642},
                {0x3ffffffff,        0x1d89d89d},
                {0x1ffffffff,        0x2fffffff},
                {0xffffffff,         0x45d1745d},
                {0x7fffffff,         0x5a5a5a5a},
                {0x3fffffff,         0x69ee5846},
                {0x1fffffff,         0x73ecade3},
                {0xfffffff,          0x79a9d260},
                {0x7ffffff,          0x7cc0532b},
                {0x3ffffff,          0x7e5ad146},
                {0x1ffffff,          0x7f2c0bec},
                {0xffffff,           0x7f95adef},
                {0x7fffff,           0x7fcac0da},
                {0x3fffff,           0x7fe55ae2},
                {0x1fffff,           0x7ff2ac0e},
                {0xfffff,            0x7ff955ae},
                {0x7ffff,            0x7ffcaac1},
                {0x3ffff,            0x7ffe555b},
                {0x1ffff,            0x7fff2aac},
                {0xffff,             0x7fff9556},
                {0x7fff,             0x7fffcaab},
                {0x3fff,             0x7fffe555},
                {0x1fff,             0x7ffff2ab},
                {0xfff,              0x7ffff955},
                {0x7ff,              0x7ffffcab},
                {0x3ff,              0x7ffffe55},
                {0x1ff,              0x7fffff2b},
                {0xff,               0x7fffff95},
                {0x7f,               0x7fffffcb},
                {0x3f,               0x7fffffe5},
                {0x1f,               0x7ffffff3},
                {0xf,                0x7ffffff9},
                {0x7,                0x7ffffffd},
                {0x3,                0x7ffffffe},
                {0x1,                0x7fffffff},
        };

        for (const auto &instance : kInputs) {
            abel::random_internal::sequence_urbg urbg({instance.first});
            EXPECT_EQ(instance.second, dist(urbg));
        }
    }

}  // namespace
